Installation

To install and load NBAMSeq

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install("NBAMSeq")
library(NBAMSeq)

Introduction

High-throughput sequencing experiments followed by differential expression analysis is a widely used approach to detect genomic biomarkers. A fundamental step in differential expression analysis is to model the association between gene counts and covariates of interest. NBAMSeq is a flexible statistical model based on the generalized additive model and allows for information sharing across genes in variance estimation. Specifically, we model the logarithm of mean gene counts as sums of smooth functions with the smoothing parameters and coefficients estimated simultaneously by a nested iteration. The variance is estimated by the Bayesian shrinkage approach to fully exploit the information across all genes.

The workflow of NBAMSeq contains three main steps:

Here we illustrate each of these steps respectively.

Data input

Users are expected to provide three parts of input, i.e. countData, colData, and design.

countData is a matrix of gene counts generated by RNASeq experiments.

## An example of countData
n = 50  ## n stands for number of genes
m = 20   ## m stands for sample size
countData = matrix(rnbinom(n*m, mu=100, size=1/3), ncol = m) + 1
mode(countData) = "integer"
colnames(countData) = paste0("sample", 1:m)
rownames(countData) = paste0("gene", 1:n)
head(countData)
      sample1 sample2 sample3 sample4 sample5 sample6 sample7 sample8 sample9
gene1       4       6     155      26       1       2       1       1       1
gene2      22       1      48      48       1     108      19       2      31
gene3     835      43      28      14       3       4     308      23      58
gene4      11     205       7     100       3       1       1     423     142
gene5      39       1     541       2     169     188     262      46       1
gene6       4      26     612       1       7       1     298       5      17
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1        1        1       34       17       93       17      210        1
gene2      496       46       18        4        7      356       25       13
gene3      102      389       34        3       77        1        3       93
gene4       62       47        8       20       70       15      118        4
gene5       29      345        1      628       53       25      114       78
gene6       56       23       10        1       69        1      105      162
      sample18 sample19 sample20
gene1       47      191        5
gene2       15       76        6
gene3        1      139       10
gene4       11      511        2
gene5        1       16       30
gene6       26       10        2

colData is a data frame which contains the covariates of samples. The sample order in colData should match the sample order in countData.

## An example of colData
pheno = runif(m, 20, 80)
var1 = rnorm(m)
var2 = rnorm(m)
var3 = rnorm(m)
var4 = as.factor(sample(c(0,1,2), m, replace = TRUE))
colData = data.frame(pheno = pheno, var1 = var1, var2 = var2,
    var3 = var3, var4 = var4)
rownames(colData) = paste0("sample", 1:m)
head(colData)
           pheno       var1        var2       var3 var4
sample1 77.16695 -2.9931128 -0.62400730 -1.0175335    2
sample2 33.19389 -0.5428027 -0.37128103 -0.9525296    2
sample3 22.91615 -0.5784937  0.44443170 -2.5807626    0
sample4 34.69313 -0.2349788  2.54787543 -0.4535905    0
sample5 53.12109 -1.3808090 -0.39424108 -0.6025536    0
sample6 48.00638 -0.3130268 -0.04284673  1.2385099    0

design is a formula which specifies how to model the samples. Compared with other packages performing DE analysis including DESeq2 (Love, Huber, and Anders 2014), edgeR (Robinson, McCarthy, and Smyth 2010), NBPSeq (Di et al. 2015) and BBSeq (Zhou, Xia, and Wright 2011), NBAMSeq supports the nonlinear model of covariates via mgcv (Wood and Wood 2015). To indicate the nonlinear covariate in the model, users are expected to use s(variable_name) in the design formula. In our example, if we would like to model pheno as a nonlinear covariate, the design formula should be:

design = ~ s(pheno) + var1 + var2 + var3 + var4

Several notes should be made regarding the design formula:

We then construct the NBAMSeqDataSet using countData, colData, and design:

gsd = NBAMSeqDataSet(countData = countData, colData = colData, design = design)
gsd
class: NBAMSeqDataSet 
dim: 50 20 
metadata(1): fitted
assays(1): counts
rownames(50): gene1 gene2 ... gene49 gene50
rowData names(0):
colnames(20): sample1 sample2 ... sample19 sample20
colData names(5): pheno var1 var2 var3 var4

Differential expression analysis

Differential expression analysis can be performed by NBAMSeq function:

gsd = NBAMSeq(gsd)

Several other arguments in NBAMSeq function are available for users to customize the analysis.

library(BiocParallel)
gsd = NBAMSeq(gsd, parallel = TRUE)

Pulling out DE results

Results of DE analysis can be pulled out by results function. For continuous covariates, the name argument should be specified indicating the covariate of interest. For nonlinear continuous covariates, base mean, effective degrees of freedom (edf), test statistics, p-value, and adjusted p-value will be returned.

res1 = results(gsd, name = "pheno")
head(res1)
DataFrame with 6 rows and 7 columns
       baseMean       edf      stat    pvalue      padj       AIC       BIC
      <numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
gene1   29.5124   1.00006 0.7447988  0.388189  0.808728   178.065   185.035
gene2   41.3324   1.00005 0.0337002  0.854472  0.968919   203.669   210.639
gene3   87.0233   1.00011 0.0278515  0.867759  0.968919   225.710   232.680
gene4   69.9674   1.00055 2.0484862  0.152685  0.477140   214.939   221.910
gene5   93.2368   1.00007 0.0515029  0.820580  0.968919   229.673   236.643
gene6   48.6789   1.00009 2.1155724  0.145816  0.477140   196.942   203.913

For linear continuous covariates, base mean, estimated coefficient, standard error, test statistics, p-value, and adjusted p-value will be returned.

res2 = results(gsd, name = "var1")
head(res2)
DataFrame with 6 rows and 8 columns
       baseMean       coef        SE       stat    pvalue      padj       AIC
      <numeric>  <numeric> <numeric>  <numeric> <numeric> <numeric> <numeric>
gene1   29.5124  0.6853972  0.364229  1.8817751 0.0598666  0.374166   178.065
gene2   41.3324  0.0232996  0.322011  0.0723567 0.9423181  0.969312   203.669
gene3   87.0233 -0.0149645  0.388979 -0.0384713 0.9693119  0.969312   225.710
gene4   69.9674  0.3540518  0.355460  0.9960371 0.3192321  0.577778   214.939
gene5   93.2368 -0.3081137  0.364491 -0.8453271 0.3979283  0.641820   229.673
gene6   48.6789  0.2165665  0.353156  0.6132325 0.5397226  0.769872   196.942
            BIC
      <numeric>
gene1   185.035
gene2   210.639
gene3   232.680
gene4   221.910
gene5   236.643
gene6   203.913

For discrete covariates, the contrast argument should be specified. e.g.  contrast = c("var4", "2", "0") means comparing level 2 vs. level 0 in var4.

res3 = results(gsd, contrast = c("var4", "2", "0"))
head(res3)
DataFrame with 6 rows and 8 columns
       baseMean      coef        SE      stat     pvalue      padj       AIC
      <numeric> <numeric> <numeric> <numeric>  <numeric> <numeric> <numeric>
gene1   29.5124 -0.627151   1.08868 -0.576065 0.56457112 0.9220420   178.065
gene2   41.3324  0.446652   0.97463  0.458278 0.64675277 0.9421056   203.669
gene3   87.0233  1.751850   1.17499  1.490954 0.13597368 0.3999226   225.710
gene4   69.9674  1.730631   1.07096  1.615968 0.10610117 0.3789328   214.939
gene5   93.2368 -3.295256   1.11540 -2.954320 0.00313358 0.0313358   229.673
gene6   48.6789 -1.581761   1.05992 -1.492344 0.13560904 0.3999226   196.942
            BIC
      <numeric>
gene1   185.035
gene2   210.639
gene3   232.680
gene4   221.910
gene5   236.643
gene6   203.913

Visualization

We suggest two approaches to visualize the nonlinear associations. The first approach is to plot the smooth components of a fitted negative binomial additive model by plot.gam function in mgcv (Wood and Wood 2015). This can be done by calling makeplot function and passing in NBAMSeqDataSet object. Users are expected to provide the phenotype of interest in phenoname argument and gene of interest in genename argument.

## assuming we are interested in the nonlinear relationship between gene10's 
## expression and "pheno"
makeplot(gsd, phenoname = "pheno", genename = "gene10", main = "gene10")

In addition, to explore the nonlinear association of covariates, it is also instructive to look at log normalized counts vs. variable scatter plot. Below we show how to produce such plot.

## here we explore the most significant nonlinear association
res1 = res1[order(res1$pvalue),]
topgene = rownames(res1)[1]  
sf = getsf(gsd)  ## get the estimated size factors
## divide raw count by size factors to obtain normalized counts
countnorm = t(t(countData)/sf) 
head(res1)
DataFrame with 6 rows and 7 columns
        baseMean       edf      stat      pvalue      padj       AIC       BIC
       <numeric> <numeric> <numeric>   <numeric> <numeric> <numeric> <numeric>
gene11   79.3169   1.00002  13.48661 0.000240205 0.0120102   205.216   212.186
gene33   53.3346   1.00022   4.78996 0.028669882 0.4710721   194.618   201.589
gene36  118.2441   1.00007   3.56999 0.058851441 0.4710721   220.179   227.150
gene35  103.4337   1.00017   3.52582 0.060482599 0.4710721   222.763   229.733
gene8    71.5521   1.00037   3.39813 0.065366652 0.4710721   223.740   230.711
gene17   67.4474   1.00005   3.03718 0.081387526 0.4710721   200.079   207.049
library(ggplot2)
setTitle = topgene
df = data.frame(pheno = pheno, logcount = log2(countnorm[topgene,]+1))
ggplot(df, aes(x=pheno, y=logcount))+geom_point(shape=19,size=1)+
    geom_smooth(method='loess')+xlab("pheno")+ylab("log(normcount + 1)")+
    annotate("text", x = max(df$pheno)-5, y = max(df$logcount)-1, 
    label = paste0("edf: ", signif(res1[topgene,"edf"],digits = 4)))+
    ggtitle(setTitle)+
    theme(text = element_text(size=10), plot.title = element_text(hjust = 0.5))

Session info

sessionInfo()
R version 4.4.0 Patched (2024-04-24 r86482)
Platform: aarch64-apple-darwin20
Running under: macOS Ventura 13.6.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/New_York
tzcode source: internal

attached base packages:
[1] stats4    stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] ggplot2_3.5.1               BiocParallel_1.37.1        
 [3] NBAMSeq_1.19.0              SummarizedExperiment_1.33.3
 [5] Biobase_2.63.1              GenomicRanges_1.55.4       
 [7] GenomeInfoDb_1.39.14        IRanges_2.37.1             
 [9] S4Vectors_0.41.7            BiocGenerics_0.49.1        
[11] MatrixGenerics_1.15.1       matrixStats_1.3.0          

loaded via a namespace (and not attached):
 [1] KEGGREST_1.43.1         gtable_0.3.5            xfun_0.43              
 [4] bslib_0.7.0             lattice_0.22-6          vctrs_0.6.5            
 [7] tools_4.4.0             generics_0.1.3          parallel_4.4.0         
[10] RSQLite_2.3.6           tibble_3.2.1            fansi_1.0.6            
[13] AnnotationDbi_1.65.2    highr_0.10              blob_1.2.4             
[16] pkgconfig_2.0.3         Matrix_1.7-0            lifecycle_1.0.4        
[19] GenomeInfoDbData_1.2.12 farver_2.1.1            compiler_4.4.0         
[22] Biostrings_2.71.6       munsell_0.5.1           DESeq2_1.43.5          
[25] codetools_0.2-20        htmltools_0.5.8.1       sass_0.4.9             
[28] yaml_2.3.8              pillar_1.9.0            crayon_1.5.2           
[31] jquerylib_0.1.4         DelayedArray_0.29.9     cachem_1.0.8           
[34] abind_1.4-5             nlme_3.1-164            genefilter_1.85.1      
[37] tidyselect_1.2.1        locfit_1.5-9.9          digest_0.6.35          
[40] dplyr_1.1.4             labeling_0.4.3          splines_4.4.0          
[43] fastmap_1.1.1           grid_4.4.0              colorspace_2.1-0       
[46] cli_3.6.2               SparseArray_1.3.7       magrittr_2.0.3         
[49] S4Arrays_1.3.7          survival_3.6-4          XML_3.99-0.16.1        
[52] utf8_1.2.4              withr_3.0.0             scales_1.3.0           
[55] UCSC.utils_0.99.7       bit64_4.0.5             rmarkdown_2.26         
[58] XVector_0.43.1          httr_1.4.7              bit_4.0.5              
[61] png_0.1-8               memoise_2.0.1           evaluate_0.23          
[64] knitr_1.46              mgcv_1.9-1              rlang_1.1.3            
[67] Rcpp_1.0.12             DBI_1.2.2               xtable_1.8-4           
[70] glue_1.7.0              annotate_1.81.2         jsonlite_1.8.8         
[73] R6_2.5.1                zlibbioc_1.49.3        

References

Di, Y, DW Schafer, JS Cumbie, and JH Chang. 2015. “NBPSeq: Negative Binomial Models for RNA-Sequencing Data.” R Package Version 0.3. 0, URL Http://CRAN. R-Project. Org/Package= NBPSeq.
Love, Michael I, Wolfgang Huber, and Simon Anders. 2014. “Moderated Estimation of Fold Change and Dispersion for RNA-Seq Data with DESeq2.” Genome Biology 15 (12): 550.
Robinson, Mark D, Davis J McCarthy, and Gordon K Smyth. 2010. “edgeR: A Bioconductor Package for Differential Expression Analysis of Digital Gene Expression Data.” Bioinformatics 26 (1): 139–40.
Wood, Simon, and Maintainer Simon Wood. 2015. “Package ’Mgcv’.” R Package Version 1: 29.
Zhou, Yi-Hui, Kai Xia, and Fred A Wright. 2011. “A Powerful and Flexible Approach to the Analysis of RNA Sequence Count Data.” Bioinformatics 27 (19): 2672–78.